Choosing Retainer Venture Class

[HEC]

But there have been speculations that HQ gear on retainers as well as making them have the highest ilvl possible also yield better rewards, would be nice to have confirmation

That's not a "speculation" but fact clearly stated in the 2.2 patch notes:

- Retainer Gear
Retainers can be equipped with gear befitting their assigned class and level, which will in turn affect items procured on their venture. Items will be procured in increased quantities by increasing either average item level for Disciples of War and Magic, or gathering rating for Disciples of the Land. Moreover, for retainers set as Disciples of the Land, increasing perception will result in a higher likelihood of obtaining high-quality items.